[PATCH] Add wording to m68k .S files to help clarify license info
[linux-3.10.git] / arch / m68k / fpsp040 / satan.S
1 |
2 |       satan.sa 3.3 12/19/90
3 |
4 |       The entry point satan computes the arctangent of an
5 |       input value. satand does the same except the input value is a
6 |       denormalized number.
7 |
8 |       Input: Double-extended value in memory location pointed to by address
9 |               register a0.
10 |
11 |       Output: Arctan(X) returned in floating-point register Fp0.
12 |
13 |       Accuracy and Monotonicity: The returned result is within 2 ulps in
14 |               64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
15 |               result is subsequently rounded to double precision. The
16 |               result is provably monotonic in double precision.
17 |
18 |       Speed: The program satan takes approximately 160 cycles for input
19 |               argument X such that 1/16 < |X| < 16. For the other arguments,
20 |               the program will run no worse than 10% slower.
21 |
22 |       Algorithm:
23 |       Step 1. If |X| >= 16 or |X| < 1/16, go to Step 5.
24 |
25 |       Step 2. Let X = sgn * 2**k * 1.xxxxxxxx...x. Note that k = -4, -3,..., or 3.
26 |               Define F = sgn * 2**k * 1.xxxx1, i.e. the first 5 significant bits
27 |               of X with a bit-1 attached at the 6-th bit position. Define u
28 |               to be u = (X-F) / (1 + X*F).
29 |
30 |       Step 3. Approximate arctan(u) by a polynomial poly.
31 |
32 |       Step 4. Return arctan(F) + poly, arctan(F) is fetched from a table of values
33 |               calculated beforehand. Exit.
34 |
35 |       Step 5. If |X| >= 16, go to Step 7.
36 |
37 |       Step 6. Approximate arctan(X) by an odd polynomial in X. Exit.
38 |
39 |       Step 7. Define X' = -1/X. Approximate arctan(X') by an odd polynomial in X'.
40 |               Arctan(X) = sign(X)*Pi/2 + arctan(X'). Exit.
41 |
42
43 |               Copyright (C) Motorola, Inc. 1990
44 |                       All Rights Reserved
45 |
46 |       For details on the license for this file, please see the
47 |       file, README, in this same directory.
48
49 |satan  idnt    2,1 | Motorola 040 Floating Point Software Package
50
51         |section        8
52
53 #include "fpsp.h"
54
55 BOUNDS1:        .long 0x3FFB8000,0x4002FFFF
56
57 ONE:    .long 0x3F800000
58
59         .long 0x00000000
60
61 ATANA3: .long 0xBFF6687E,0x314987D8
62 ATANA2: .long 0x4002AC69,0x34A26DB3
63
64 ATANA1: .long 0xBFC2476F,0x4E1DA28E
65 ATANB6: .long 0x3FB34444,0x7F876989
66
67 ATANB5: .long 0xBFB744EE,0x7FAF45DB
68 ATANB4: .long 0x3FBC71C6,0x46940220
69
70 ATANB3: .long 0xBFC24924,0x921872F9
71 ATANB2: .long 0x3FC99999,0x99998FA9
72
73 ATANB1: .long 0xBFD55555,0x55555555
74 ATANC5: .long 0xBFB70BF3,0x98539E6A
75
76 ATANC4: .long 0x3FBC7187,0x962D1D7D
77 ATANC3: .long 0xBFC24924,0x827107B8
78
79 ATANC2: .long 0x3FC99999,0x9996263E
80 ATANC1: .long 0xBFD55555,0x55555536
81
82 PPIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
83 NPIBY2: .long 0xBFFF0000,0xC90FDAA2,0x2168C235,0x00000000
84 PTINY:  .long 0x00010000,0x80000000,0x00000000,0x00000000
85 NTINY:  .long 0x80010000,0x80000000,0x00000000,0x00000000
86
87 ATANTBL:
88         .long   0x3FFB0000,0x83D152C5,0x060B7A51,0x00000000
89         .long   0x3FFB0000,0x8BC85445,0x65498B8B,0x00000000
90         .long   0x3FFB0000,0x93BE4060,0x17626B0D,0x00000000
91         .long   0x3FFB0000,0x9BB3078D,0x35AEC202,0x00000000
92         .long   0x3FFB0000,0xA3A69A52,0x5DDCE7DE,0x00000000
93         .long   0x3FFB0000,0xAB98E943,0x62765619,0x00000000
94         .long   0x3FFB0000,0xB389E502,0xF9C59862,0x00000000
95         .long   0x3FFB0000,0xBB797E43,0x6B09E6FB,0x00000000
96         .long   0x3FFB0000,0xC367A5C7,0x39E5F446,0x00000000
97         .long   0x3FFB0000,0xCB544C61,0xCFF7D5C6,0x00000000
98         .long   0x3FFB0000,0xD33F62F8,0x2488533E,0x00000000
99         .long   0x3FFB0000,0xDB28DA81,0x62404C77,0x00000000
100         .long   0x3FFB0000,0xE310A407,0x8AD34F18,0x00000000
101         .long   0x3FFB0000,0xEAF6B0A8,0x188EE1EB,0x00000000
102         .long   0x3FFB0000,0xF2DAF194,0x9DBE79D5,0x00000000
103         .long   0x3FFB0000,0xFABD5813,0x61D47E3E,0x00000000
104         .long   0x3FFC0000,0x8346AC21,0x0959ECC4,0x00000000
105         .long   0x3FFC0000,0x8B232A08,0x304282D8,0x00000000
106         .long   0x3FFC0000,0x92FB70B8,0xD29AE2F9,0x00000000
107         .long   0x3FFC0000,0x9ACF476F,0x5CCD1CB4,0x00000000
108         .long   0x3FFC0000,0xA29E7630,0x4954F23F,0x00000000
109         .long   0x3FFC0000,0xAA68C5D0,0x8AB85230,0x00000000
110         .long   0x3FFC0000,0xB22DFFFD,0x9D539F83,0x00000000
111         .long   0x3FFC0000,0xB9EDEF45,0x3E900EA5,0x00000000
112         .long   0x3FFC0000,0xC1A85F1C,0xC75E3EA5,0x00000000
113         .long   0x3FFC0000,0xC95D1BE8,0x28138DE6,0x00000000
114         .long   0x3FFC0000,0xD10BF300,0x840D2DE4,0x00000000
115         .long   0x3FFC0000,0xD8B4B2BA,0x6BC05E7A,0x00000000
116         .long   0x3FFC0000,0xE0572A6B,0xB42335F6,0x00000000
117         .long   0x3FFC0000,0xE7F32A70,0xEA9CAA8F,0x00000000
118         .long   0x3FFC0000,0xEF888432,0x64ECEFAA,0x00000000
119         .long   0x3FFC0000,0xF7170A28,0xECC06666,0x00000000
120         .long   0x3FFD0000,0x812FD288,0x332DAD32,0x00000000
121         .long   0x3FFD0000,0x88A8D1B1,0x218E4D64,0x00000000
122         .long   0x3FFD0000,0x9012AB3F,0x23E4AEE8,0x00000000
123         .long   0x3FFD0000,0x976CC3D4,0x11E7F1B9,0x00000000
124         .long   0x3FFD0000,0x9EB68949,0x3889A227,0x00000000
125         .long   0x3FFD0000,0xA5EF72C3,0x4487361B,0x00000000
126         .long   0x3FFD0000,0xAD1700BA,0xF07A7227,0x00000000
127         .long   0x3FFD0000,0xB42CBCFA,0xFD37EFB7,0x00000000
128         .long   0x3FFD0000,0xBB303A94,0x0BA80F89,0x00000000
129         .long   0x3FFD0000,0xC22115C6,0xFCAEBBAF,0x00000000
130         .long   0x3FFD0000,0xC8FEF3E6,0x86331221,0x00000000
131         .long   0x3FFD0000,0xCFC98330,0xB4000C70,0x00000000
132         .long   0x3FFD0000,0xD6807AA1,0x102C5BF9,0x00000000
133         .long   0x3FFD0000,0xDD2399BC,0x31252AA3,0x00000000
134         .long   0x3FFD0000,0xE3B2A855,0x6B8FC517,0x00000000
135         .long   0x3FFD0000,0xEA2D764F,0x64315989,0x00000000
136         .long   0x3FFD0000,0xF3BF5BF8,0xBAD1A21D,0x00000000
137         .long   0x3FFE0000,0x801CE39E,0x0D205C9A,0x00000000
138         .long   0x3FFE0000,0x8630A2DA,0xDA1ED066,0x00000000
139         .long   0x3FFE0000,0x8C1AD445,0xF3E09B8C,0x00000000
140         .long   0x3FFE0000,0x91DB8F16,0x64F350E2,0x00000000
141         .long   0x3FFE0000,0x97731420,0x365E538C,0x00000000
142         .long   0x3FFE0000,0x9CE1C8E6,0xA0B8CDBA,0x00000000
143         .long   0x3FFE0000,0xA22832DB,0xCADAAE09,0x00000000
144         .long   0x3FFE0000,0xA746F2DD,0xB7602294,0x00000000
145         .long   0x3FFE0000,0xAC3EC0FB,0x997DD6A2,0x00000000
146         .long   0x3FFE0000,0xB110688A,0xEBDC6F6A,0x00000000
147         .long   0x3FFE0000,0xB5BCC490,0x59ECC4B0,0x00000000
148         .long   0x3FFE0000,0xBA44BC7D,0xD470782F,0x00000000
149         .long   0x3FFE0000,0xBEA94144,0xFD049AAC,0x00000000
150         .long   0x3FFE0000,0xC2EB4ABB,0x661628B6,0x00000000
151         .long   0x3FFE0000,0xC70BD54C,0xE602EE14,0x00000000
152         .long   0x3FFE0000,0xCD000549,0xADEC7159,0x00000000
153         .long   0x3FFE0000,0xD48457D2,0xD8EA4EA3,0x00000000
154         .long   0x3FFE0000,0xDB948DA7,0x12DECE3B,0x00000000
155         .long   0x3FFE0000,0xE23855F9,0x69E8096A,0x00000000
156         .long   0x3FFE0000,0xE8771129,0xC4353259,0x00000000
157         .long   0x3FFE0000,0xEE57C16E,0x0D379C0D,0x00000000
158         .long   0x3FFE0000,0xF3E10211,0xA87C3779,0x00000000
159         .long   0x3FFE0000,0xF919039D,0x758B8D41,0x00000000
160         .long   0x3FFE0000,0xFE058B8F,0x64935FB3,0x00000000
161         .long   0x3FFF0000,0x8155FB49,0x7B685D04,0x00000000
162         .long   0x3FFF0000,0x83889E35,0x49D108E1,0x00000000
163         .long   0x3FFF0000,0x859CFA76,0x511D724B,0x00000000
164         .long   0x3FFF0000,0x87952ECF,0xFF8131E7,0x00000000
165         .long   0x3FFF0000,0x89732FD1,0x9557641B,0x00000000
166         .long   0x3FFF0000,0x8B38CAD1,0x01932A35,0x00000000
167         .long   0x3FFF0000,0x8CE7A8D8,0x301EE6B5,0x00000000
168         .long   0x3FFF0000,0x8F46A39E,0x2EAE5281,0x00000000
169         .long   0x3FFF0000,0x922DA7D7,0x91888487,0x00000000
170         .long   0x3FFF0000,0x94D19FCB,0xDEDF5241,0x00000000
171         .long   0x3FFF0000,0x973AB944,0x19D2A08B,0x00000000
172         .long   0x3FFF0000,0x996FF00E,0x08E10B96,0x00000000
173         .long   0x3FFF0000,0x9B773F95,0x12321DA7,0x00000000
174         .long   0x3FFF0000,0x9D55CC32,0x0F935624,0x00000000
175         .long   0x3FFF0000,0x9F100575,0x006CC571,0x00000000
176         .long   0x3FFF0000,0xA0A9C290,0xD97CC06C,0x00000000
177         .long   0x3FFF0000,0xA22659EB,0xEBC0630A,0x00000000
178         .long   0x3FFF0000,0xA388B4AF,0xF6EF0EC9,0x00000000
179         .long   0x3FFF0000,0xA4D35F10,0x61D292C4,0x00000000
180         .long   0x3FFF0000,0xA60895DC,0xFBE3187E,0x00000000
181         .long   0x3FFF0000,0xA72A51DC,0x7367BEAC,0x00000000
182         .long   0x3FFF0000,0xA83A5153,0x0956168F,0x00000000
183         .long   0x3FFF0000,0xA93A2007,0x7539546E,0x00000000
184         .long   0x3FFF0000,0xAA9E7245,0x023B2605,0x00000000
185         .long   0x3FFF0000,0xAC4C84BA,0x6FE4D58F,0x00000000
186         .long   0x3FFF0000,0xADCE4A4A,0x606B9712,0x00000000
187         .long   0x3FFF0000,0xAF2A2DCD,0x8D263C9C,0x00000000
188         .long   0x3FFF0000,0xB0656F81,0xF22265C7,0x00000000
189         .long   0x3FFF0000,0xB1846515,0x0F71496A,0x00000000
190         .long   0x3FFF0000,0xB28AAA15,0x6F9ADA35,0x00000000
191         .long   0x3FFF0000,0xB37B44FF,0x3766B895,0x00000000
192         .long   0x3FFF0000,0xB458C3DC,0xE9630433,0x00000000
193         .long   0x3FFF0000,0xB525529D,0x562246BD,0x00000000
194         .long   0x3FFF0000,0xB5E2CCA9,0x5F9D88CC,0x00000000
195         .long   0x3FFF0000,0xB692CADA,0x7ACA1ADA,0x00000000
196         .long   0x3FFF0000,0xB736AEA7,0xA6925838,0x00000000
197         .long   0x3FFF0000,0xB7CFAB28,0x7E9F7B36,0x00000000
198         .long   0x3FFF0000,0xB85ECC66,0xCB219835,0x00000000
199         .long   0x3FFF0000,0xB8E4FD5A,0x20A593DA,0x00000000
200         .long   0x3FFF0000,0xB99F41F6,0x4AFF9BB5,0x00000000
201         .long   0x3FFF0000,0xBA7F1E17,0x842BBE7B,0x00000000
202         .long   0x3FFF0000,0xBB471285,0x7637E17D,0x00000000
203         .long   0x3FFF0000,0xBBFABE8A,0x4788DF6F,0x00000000
204         .long   0x3FFF0000,0xBC9D0FAD,0x2B689D79,0x00000000
205         .long   0x3FFF0000,0xBD306A39,0x471ECD86,0x00000000
206         .long   0x3FFF0000,0xBDB6C731,0x856AF18A,0x00000000
207         .long   0x3FFF0000,0xBE31CAC5,0x02E80D70,0x00000000
208         .long   0x3FFF0000,0xBEA2D55C,0xE33194E2,0x00000000
209         .long   0x3FFF0000,0xBF0B10B7,0xC03128F0,0x00000000
210         .long   0x3FFF0000,0xBF6B7A18,0xDACB778D,0x00000000
211         .long   0x3FFF0000,0xBFC4EA46,0x63FA18F6,0x00000000
212         .long   0x3FFF0000,0xC0181BDE,0x8B89A454,0x00000000
213         .long   0x3FFF0000,0xC065B066,0xCFBF6439,0x00000000
214         .long   0x3FFF0000,0xC0AE345F,0x56340AE6,0x00000000
215         .long   0x3FFF0000,0xC0F22291,0x9CB9E6A7,0x00000000
216
217         .set    X,FP_SCR1
218         .set    XDCARE,X+2
219         .set    XFRAC,X+4
220         .set    XFRACLO,X+8
221
222         .set    ATANF,FP_SCR2
223         .set    ATANFHI,ATANF+4
224         .set    ATANFLO,ATANF+8
225
226
227         | xref  t_frcinx
228         |xref   t_extdnrm
229
230         .global satand
231 satand:
232 |--ENTRY POINT FOR ATAN(X) FOR DENORMALIZED ARGUMENT
233
234         bra             t_extdnrm
235
236         .global satan
237 satan:
238 |--ENTRY POINT FOR ATAN(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
239
240         fmovex          (%a0),%fp0      | ...LOAD INPUT
241
242         movel           (%a0),%d0
243         movew           4(%a0),%d0
244         fmovex          %fp0,X(%a6)
245         andil           #0x7FFFFFFF,%d0
246
247         cmpil           #0x3FFB8000,%d0         | ...|X| >= 1/16?
248         bges            ATANOK1
249         bra             ATANSM
250
251 ATANOK1:
252         cmpil           #0x4002FFFF,%d0         | ...|X| < 16 ?
253         bles            ATANMAIN
254         bra             ATANBIG
255
256
257 |--THE MOST LIKELY CASE, |X| IN [1/16, 16). WE USE TABLE TECHNIQUE
258 |--THE IDEA IS ATAN(X) = ATAN(F) + ATAN( [X-F] / [1+XF] ).
259 |--SO IF F IS CHOSEN TO BE CLOSE TO X AND ATAN(F) IS STORED IN
260 |--A TABLE, ALL WE NEED IS TO APPROXIMATE ATAN(U) WHERE
261 |--U = (X-F)/(1+XF) IS SMALL (REMEMBER F IS CLOSE TO X). IT IS
262 |--TRUE THAT A DIVIDE IS NOW NEEDED, BUT THE APPROXIMATION FOR
263 |--ATAN(U) IS A VERY SHORT POLYNOMIAL AND THE INDEXING TO
264 |--FETCH F AND SAVING OF REGISTERS CAN BE ALL HIDED UNDER THE
265 |--DIVIDE. IN THE END THIS METHOD IS MUCH FASTER THAN A TRADITIONAL
266 |--ONE. NOTE ALSO THAT THE TRADITIONAL SCHEME THAT APPROXIMATE
267 |--ATAN(X) DIRECTLY WILL NEED TO USE A RATIONAL APPROXIMATION
268 |--(DIVISION NEEDED) ANYWAY BECAUSE A POLYNOMIAL APPROXIMATION
269 |--WILL INVOLVE A VERY LONG POLYNOMIAL.
270
271 |--NOW WE SEE X AS +-2^K * 1.BBBBBBB....B <- 1. + 63 BITS
272 |--WE CHOSE F TO BE +-2^K * 1.BBBB1
273 |--THAT IS IT MATCHES THE EXPONENT AND FIRST 5 BITS OF X, THE
274 |--SIXTH BITS IS SET TO BE 1. SINCE K = -4, -3, ..., 3, THERE
275 |--ARE ONLY 8 TIMES 16 = 2^7 = 128 |F|'S. SINCE ATAN(-|F|) IS
276 |-- -ATAN(|F|), WE NEED TO STORE ONLY ATAN(|F|).
277
278 ATANMAIN:
279
280         movew           #0x0000,XDCARE(%a6)     | ...CLEAN UP X JUST IN CASE
281         andil           #0xF8000000,XFRAC(%a6)  | ...FIRST 5 BITS
282         oril            #0x04000000,XFRAC(%a6)  | ...SET 6-TH BIT TO 1
283         movel           #0x00000000,XFRACLO(%a6)        | ...LOCATION OF X IS NOW F
284
285         fmovex          %fp0,%fp1                       | ...FP1 IS X
286         fmulx           X(%a6),%fp1             | ...FP1 IS X*F, NOTE THAT X*F > 0
287         fsubx           X(%a6),%fp0             | ...FP0 IS X-F
288         fadds           #0x3F800000,%fp1                | ...FP1 IS 1 + X*F
289         fdivx           %fp1,%fp0                       | ...FP0 IS U = (X-F)/(1+X*F)
290
291 |--WHILE THE DIVISION IS TAKING ITS TIME, WE FETCH ATAN(|F|)
292 |--CREATE ATAN(F) AND STORE IT IN ATANF, AND
293 |--SAVE REGISTERS FP2.
294
295         movel           %d2,-(%a7)      | ...SAVE d2 TEMPORARILY
296         movel           %d0,%d2         | ...THE EXPO AND 16 BITS OF X
297         andil           #0x00007800,%d0 | ...4 VARYING BITS OF F'S FRACTION
298         andil           #0x7FFF0000,%d2 | ...EXPONENT OF F
299         subil           #0x3FFB0000,%d2 | ...K+4
300         asrl            #1,%d2
301         addl            %d2,%d0         | ...THE 7 BITS IDENTIFYING F
302         asrl            #7,%d0          | ...INDEX INTO TBL OF ATAN(|F|)
303         lea             ATANTBL,%a1
304         addal           %d0,%a1         | ...ADDRESS OF ATAN(|F|)
305         movel           (%a1)+,ATANF(%a6)
306         movel           (%a1)+,ATANFHI(%a6)
307         movel           (%a1)+,ATANFLO(%a6)     | ...ATANF IS NOW ATAN(|F|)
308         movel           X(%a6),%d0              | ...LOAD SIGN AND EXPO. AGAIN
309         andil           #0x80000000,%d0 | ...SIGN(F)
310         orl             %d0,ATANF(%a6)  | ...ATANF IS NOW SIGN(F)*ATAN(|F|)
311         movel           (%a7)+,%d2      | ...RESTORE d2
312
313 |--THAT'S ALL I HAVE TO DO FOR NOW,
314 |--BUT ALAS, THE DIVIDE IS STILL CRANKING!
315
316 |--U IN FP0, WE ARE NOW READY TO COMPUTE ATAN(U) AS
317 |--U + A1*U*V*(A2 + V*(A3 + V)), V = U*U
318 |--THE POLYNOMIAL MAY LOOK STRANGE, BUT IS NEVERTHELESS CORRECT.
319 |--THE NATURAL FORM IS U + U*V*(A1 + V*(A2 + V*A3))
320 |--WHAT WE HAVE HERE IS MERELY  A1 = A3, A2 = A1/A3, A3 = A2/A3.
321 |--THE REASON FOR THIS REARRANGEMENT IS TO MAKE THE INDEPENDENT
322 |--PARTS A1*U*V AND (A2 + ... STUFF) MORE LOAD-BALANCED
323
324
325         fmovex          %fp0,%fp1
326         fmulx           %fp1,%fp1
327         fmoved          ATANA3,%fp2
328         faddx           %fp1,%fp2               | ...A3+V
329         fmulx           %fp1,%fp2               | ...V*(A3+V)
330         fmulx           %fp0,%fp1               | ...U*V
331         faddd           ATANA2,%fp2     | ...A2+V*(A3+V)
332         fmuld           ATANA1,%fp1     | ...A1*U*V
333         fmulx           %fp2,%fp1               | ...A1*U*V*(A2+V*(A3+V))
334
335         faddx           %fp1,%fp0               | ...ATAN(U), FP1 RELEASED
336         fmovel          %d1,%FPCR               |restore users exceptions
337         faddx           ATANF(%a6),%fp0 | ...ATAN(X)
338         bra             t_frcinx
339
340 ATANBORS:
341 |--|X| IS IN d0 IN COMPACT FORM. FP1, d0 SAVED.
342 |--FP0 IS X AND |X| <= 1/16 OR |X| >= 16.
343         cmpil           #0x3FFF8000,%d0
344         bgt             ATANBIG | ...I.E. |X| >= 16
345
346 ATANSM:
347 |--|X| <= 1/16
348 |--IF |X| < 2^(-40), RETURN X AS ANSWER. OTHERWISE, APPROXIMATE
349 |--ATAN(X) BY X + X*Y*(B1+Y*(B2+Y*(B3+Y*(B4+Y*(B5+Y*B6)))))
350 |--WHICH IS X + X*Y*( [B1+Z*(B3+Z*B5)] + [Y*(B2+Z*(B4+Z*B6)] )
351 |--WHERE Y = X*X, AND Z = Y*Y.
352
353         cmpil           #0x3FD78000,%d0
354         blt             ATANTINY
355 |--COMPUTE POLYNOMIAL
356         fmulx           %fp0,%fp0       | ...FP0 IS Y = X*X
357
358
359         movew           #0x0000,XDCARE(%a6)
360
361         fmovex          %fp0,%fp1
362         fmulx           %fp1,%fp1               | ...FP1 IS Z = Y*Y
363
364         fmoved          ATANB6,%fp2
365         fmoved          ATANB5,%fp3
366
367         fmulx           %fp1,%fp2               | ...Z*B6
368         fmulx           %fp1,%fp3               | ...Z*B5
369
370         faddd           ATANB4,%fp2     | ...B4+Z*B6
371         faddd           ATANB3,%fp3     | ...B3+Z*B5
372
373         fmulx           %fp1,%fp2               | ...Z*(B4+Z*B6)
374         fmulx           %fp3,%fp1               | ...Z*(B3+Z*B5)
375
376         faddd           ATANB2,%fp2     | ...B2+Z*(B4+Z*B6)
377         faddd           ATANB1,%fp1     | ...B1+Z*(B3+Z*B5)
378
379         fmulx           %fp0,%fp2               | ...Y*(B2+Z*(B4+Z*B6))
380         fmulx           X(%a6),%fp0             | ...X*Y
381
382         faddx           %fp2,%fp1               | ...[B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]
383
384
385         fmulx           %fp1,%fp0       | ...X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))])
386
387         fmovel          %d1,%FPCR               |restore users exceptions
388         faddx           X(%a6),%fp0
389
390         bra             t_frcinx
391
392 ATANTINY:
393 |--|X| < 2^(-40), ATAN(X) = X
394         movew           #0x0000,XDCARE(%a6)
395
396         fmovel          %d1,%FPCR               |restore users exceptions
397         fmovex          X(%a6),%fp0     |last inst - possible exception set
398
399         bra             t_frcinx
400
401 ATANBIG:
402 |--IF |X| > 2^(100), RETURN     SIGN(X)*(PI/2 - TINY). OTHERWISE,
403 |--RETURN SIGN(X)*PI/2 + ATAN(-1/X).
404         cmpil           #0x40638000,%d0
405         bgt             ATANHUGE
406
407 |--APPROXIMATE ATAN(-1/X) BY
408 |--X'+X'*Y*(C1+Y*(C2+Y*(C3+Y*(C4+Y*C5)))), X' = -1/X, Y = X'*X'
409 |--THIS CAN BE RE-WRITTEN AS
410 |--X'+X'*Y*( [C1+Z*(C3+Z*C5)] + [Y*(C2+Z*C4)] ), Z = Y*Y.
411
412         fmoves          #0xBF800000,%fp1        | ...LOAD -1
413         fdivx           %fp0,%fp1               | ...FP1 IS -1/X
414
415
416 |--DIVIDE IS STILL CRANKING
417
418         fmovex          %fp1,%fp0               | ...FP0 IS X'
419         fmulx           %fp0,%fp0               | ...FP0 IS Y = X'*X'
420         fmovex          %fp1,X(%a6)             | ...X IS REALLY X'
421
422         fmovex          %fp0,%fp1
423         fmulx           %fp1,%fp1               | ...FP1 IS Z = Y*Y
424
425         fmoved          ATANC5,%fp3
426         fmoved          ATANC4,%fp2
427
428         fmulx           %fp1,%fp3               | ...Z*C5
429         fmulx           %fp1,%fp2               | ...Z*B4
430
431         faddd           ATANC3,%fp3     | ...C3+Z*C5
432         faddd           ATANC2,%fp2     | ...C2+Z*C4
433
434         fmulx           %fp3,%fp1               | ...Z*(C3+Z*C5), FP3 RELEASED
435         fmulx           %fp0,%fp2               | ...Y*(C2+Z*C4)
436
437         faddd           ATANC1,%fp1     | ...C1+Z*(C3+Z*C5)
438         fmulx           X(%a6),%fp0             | ...X'*Y
439
440         faddx           %fp2,%fp1               | ...[Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)]
441
442
443         fmulx           %fp1,%fp0               | ...X'*Y*([B1+Z*(B3+Z*B5)]
444 |                                       ...     +[Y*(B2+Z*(B4+Z*B6))])
445         faddx           X(%a6),%fp0
446
447         fmovel          %d1,%FPCR               |restore users exceptions
448
449         btstb           #7,(%a0)
450         beqs            pos_big
451
452 neg_big:
453         faddx           NPIBY2,%fp0
454         bra             t_frcinx
455
456 pos_big:
457         faddx           PPIBY2,%fp0
458         bra             t_frcinx
459
460 ATANHUGE:
461 |--RETURN SIGN(X)*(PIBY2 - TINY) = SIGN(X)*PIBY2 - SIGN(X)*TINY
462         btstb           #7,(%a0)
463         beqs            pos_huge
464
465 neg_huge:
466         fmovex          NPIBY2,%fp0
467         fmovel          %d1,%fpcr
468         fsubx           NTINY,%fp0
469         bra             t_frcinx
470
471 pos_huge:
472         fmovex          PPIBY2,%fp0
473         fmovel          %d1,%fpcr
474         fsubx           PTINY,%fp0
475         bra             t_frcinx
476
477         |end